Abstract The goal of this research is to develop new multivariate data analysis techniques for neural recordings that reveal causal dependencies between recording sites. Delay Differential Analysis (DDA) is a robust and ef?cient nonlinear time-domain algorithm for time series data that complements linear spectral methods. DDA combines delay and differential embeddings in nonlinear dynamical systems to discriminate between different normal and abnormal cortical states with high temporal resolution and insensitivity to artifacts. The proposed research generalizes Granger causality for linear systems by developing a cross-dynamical version of DDA (CD-DDA) to measure the ?ow of information between brain areas. This is an important problem for which existing approaches are inadequate. CD-DDA will be applied ?rst to simulations of cortical network models with Hodgkin-Huxley neurons, where causal in?uence can be controlled and the ef?cacy of CD-DDA can be validated. In collaboration with Sydney Cash at the Massachusetts General Hospital, CD-DDA will then be applied to electrocorticography (ECoG) recordings from human epilepsy patients with implanted grids of electrodes. We previously analyzed these recordings with DDA, which revealed differences between cortical states leading up to seizures, abrupt shifts at the onsets of the seizures and altered cortical states long after the seizures. These ECoG recordings will be re-analyzed using CD-DDA, which should reveal how communication between cortical areas recon?gures before seizures. We also have access to many hours of interictal recordings, which will give us the opportunity to establish a baseline for how information ?ows in cortical circuits during more normal cortical activity. We will make the software for all of the DDA algorithms we have developed openly available. These new algorithms will have many other applications for analyzing neural signals online in other brain areas and from other neural time series, including calcium ?uorescence imaging from single cells, dendrites and synapses and recordings using voltage-sensitive dyes.